Blog

adsense

Given the function \(y = f\left( x \right)\) have derivatives \(f’\left( x \right) = {\left( {x – 2} \right)^2}\left( {1 – x} \right)\) with everyone \(x \in \mathbb{R}\). The given function is covariate on which of the following intervals?

A. \(\left( {1;2} \right)\).

B. \(\left( {1; + \infty } \right)\).

C. \(\left( {2; + \infty } \right)\).

D. \(\left( { – \infty ;1} \right)\).

adsense

The answer:

Choose EASY

We have \(f’\left( x \right) > 0 \Leftrightarrow {\left( {x – 2} \right)^2}\left( {1 – x} \right) > 0 \Leftrightarrow \left\{ \ begin{array}{l}1 – x > 0\\{\left( {x – 2} \right)^2} > 0\end{array} \right \Leftrightarrow \left\{ \begin{array} {l}x < 1\\x \ne 2\end{array} \right. \Leftrightarrow x < 1\).

So the function is covariant on the interval \(\left( { – \infty ;1} \right)\).